To go from Yosemite to Bryce in a day would indeed be a long day. You could make things a little easier by finishing your visit in Yosemite with a drive back over Tioga Pass and lodge in Lee Vining. You could also look to make Zion your first port of call, Springdale is a great little town with lodging options. You could look around next day and take the Mt Carmel tunnel to Bryce canyon and then the following day head to the North rim.

It would help to give the best possible advice if we were to see the full picture of your trip and how long you have rather than bits and pieces of it.